Theorem syl2an23an

Description: Deduction related to syl3an with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016) (Proof shortened by Wolf Lammen, 28-Jun-2022)

	Ref	Expression
Hypotheses	syl2an23an.1	|- ( ph -> ps )
	syl2an23an.2	|- ( ph -> ch )
	syl2an23an.3	|- ( ( th /\ ph ) -> ta )
	syl2an23an.4	|- ( ( ps /\ ch /\ ta ) -> et )
Assertion	syl2an23an	|- ( ( th /\ ph ) -> et )

Proof

Step	Hyp	Ref	Expression
1		syl2an23an.1	|- ( ph -> ps )
2		syl2an23an.2	|- ( ph -> ch )
3		syl2an23an.3	|- ( ( th /\ ph ) -> ta )
4		syl2an23an.4	|- ( ( ps /\ ch /\ ta ) -> et )
5	1 2 3 4	syl2an3an	|- ( ( ph /\ ( th /\ ph ) ) -> et )
6	5	anabss7	|- ( ( th /\ ph ) -> et )